Propagation des ondes dans un domaine comportant des petites hétérogénéités : modélisation asymptotique et calcul numérique

Vanessa Mattesi 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : In this thesis, we focus our attention on the modeling of heterogeneities which are smaller than the wavelength. The document is decomposed into two parts : a theoretical one and a numerical one. In the first part, we derive a matched asymptotic expansion composed of a far-field expansion and a near-field expansion. The terms of the far-field expansion are singular solutions of the wave equation whereas the terms of the near-field expansion satisfy quasistatic problems. These expansions are matched in an intermediate region. We justify mathematically this theory by proving error estimates. In the second part, we describe the Discontinuous Galerkin method, a local time stepping method and the implementation of the matched asymptotic method. Numerical simulations illustrate these results.
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https://hal.inria.fr/tel-01111046
Contributor : Vanessa Mattesi <>
Submitted on : Thursday, January 29, 2015 - 3:03:05 PM
Last modification on : Sunday, April 7, 2019 - 3:00:03 PM
Long-term archiving on : Wednesday, May 27, 2015 - 2:00:41 PM

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  • HAL Id : tel-01111046, version 1

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Vanessa Mattesi. Propagation des ondes dans un domaine comportant des petites hétérogénéités : modélisation asymptotique et calcul numérique. Analyse numérique [math.NA]. Université de Pau et des pays de l'Adour, 2014. Français. ⟨tel-01111046⟩

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